Microwire transmission line

Online calculator

2022-12-20 Revised 2026-02-12

Takayuki HOSODA

Microwire transmission line calculator

Frequency MHz

Electrical length deg

Dielectric relative permittivity (ε_r )

Dielectric thickness (h ) μm

Conductor diameter (d) μm

Impedance (Z₀) ≈ Ω

Effective permittivity (Ε_eff) ≈

Capacitance ≈    pF/m

Inductance ≈    nH/m

Velocity of propagation ≈

Phisical length ≈    mm

zmicrowire - Analyze microwire transmission line. Rev.0.3 (Feb. 12, 2026) (c) 2022 Takayuki HOSODA

Formulas used ^[1]

$\varepsilon_{eff} &=& \frac{\varepsilon_{r} + 1}{2} + \frac{\varepsilon_{r} - 1}{2}\left(\sqrt{\frac{d}{d + 12 h}} + \Delta \right) \\ \Delta &=& \left\{ \begin{array}{ll} 0.04 \left(1 - \displaystyle\frac{d}{h}\right)^2 \qquad &\text { if $d < h$,}\\ 0 & \text{ if $d \geq h$} \end{array} \right.\\ Z_0 &=& \frac{ \mu_0 c} {2 \pi \sqrt {\varepsilon_{eff}} }\ \cosh^{-1} \left(\displaystyle\frac{2h}{d}\right)$

where
η₀: characteristic impedance of vacuum of free space 376.730313668(57) Ω (CODATA 2022)

APPENDIX

Example of electric field solver results

microwireline electric field visualizathin

REFERENCE

Brian C. Wadell, Transmission Line Design Handbook, Artech House, 1991, ISBN 0-89006-436-9.
IPC, IPC-2141A: Design Guide for High-Speed Controlled Impedance Circuit Boards, IPC-2141A, March 2004.
NIST, Fundamental Physical Constants .

Frequency	MHz
Electrical length	deg
*Dielectric relative permittivity (ε_r* )**
Dielectric thickness (h )	μm
Conductor diameter (d)	μm
Impedance (Z₀) ≈	Ω
Effective permittivity (Ε_eff) ≈
Capacitance ≈	pF/m
Inductance ≈	nH/m
Velocity of propagation ≈
Phisical length ≈	mm

Microwire transmission line

Microwire transmission line calculator

Formulas used [1]

APPENDIX

Example of electric field solver results

REFERENCE

SEE ALSO

Formulas used ^[1]